Three-step alternating and preconditioned scheme for rectangular matrices

  • Ashish Kumar Nandi
  • Jajati Keshari SahooEmail author
  • Pushpendu Ghosh
Original Research


In this article, a three-step alternating iterative scheme for rectangular system has been proposed. The convergence and comparison analysis of the proposed method has been discussed for the class of semi-monotone matrices and which confirms the faster convergence of our scheme. A preconditioned approach is also presented in this paper to relax the semi-monotonicity condition. The preconditioned approach is very promising and converges faster than some of existing schemes. We finally validated all the theoretical results by some numerical examples.


Nonnegativity Moore–Penrose inverse Semi-monotone Proper splitting Convergence theorem Comparison theorem 

Mathematics Subject Classification

15A09 65F10 65F15 65F20 



We would like to thank Dr. Chinmay Kumar Giri, Lecturer, Department of Mathematics, Govt. Women’s College Baripada, India for his helpful suggestions. The authors also thank the referee for his/her helpful comments and suggestions which led to a much improved presentation of the paper.


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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.Department of MathematicsBITS Pilani, K.K. Birla Goa CampusGoaIndia
  2. 2.Department of Computer Science and Information SystemsBITS Pilani, K.K. Birla Goa CampusGoaIndia

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